With a known thread cutting head of this type, an automatic opening occurs in such a way that, after reaching a predetermined thread cutting length, the pipe end strikes against an unlocking or unlatching abutment, by means of which the arresting of the pretensioned control disc is released. As a result, the control disc shifts relative to the cutting-jaw holder due to its pretensioning force, and the cutting jaws lift off radially from the thread and release the pipe end. In this instance, the clamping or tensioning lever, embodied as a kind of knee-lever, is pivotally journalled on the outer periphery of the cutting-jaw holder and, in its arresting position, is under the force of a spring bolt. The disadvantage of this thread bolt consists therein that, during release by the unlatching abutment, the tensioning lever, due to the force of the spring bolt, jumps radially upwardly in a sudden manner in the plane of the cutting-jaw holder, so that with every thread cutting process at the moment of opening of the cutting head there exists a considerable danger of accidents which, especially with bent-forward working position of the operator, can cause facial injury. A further disadvantage consists therein that the latching and knee-lever mechanism of the tensioning lever is costly and susceptible to dirt accumulation, whereby a susceptibility to disturbances is created, and that a pinching of the operator's fingers can occur at the knee-lever structure when pressing-down the tensioning lever into the arresting position, so that also with this working step a danger of injury exists.